For the following question, assume that lines that appear to be tangent are tangent. Point O is the center of the circle. Find the value of x. ∡O = 142° (1 point)

Question

For the following question, assume that lines that appear to be tangent are tangent. Point O is the center of the circle. Find the value of x. ∡O = 142° (1 point)

Responses Choose 1:
38
58
44
218

Answer 1

58

Explanation: The angle formed by a chord and a tangent line going through the point of contact is always equal to 1/2 the central angle. Therefore, x = (1/2)(142) = 71 degrees. Since the sum of the angles in a triangle is 180 degrees, the remaining angle in the triangle is 180 - 71 - 51 = 58 degrees.